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An AR(2) time series, {x,: t€T}, if | 7₁ |>1 and | 7₂ |>1, where ₁ and 2 are the roots ofthe polynomial 1 - B₁ x - ₂x² = 0. Show that an AR(2) time series is stationary if the parameters, ß₁ and ß2, satisfy the following inequalities: B₂+ B1 <1, B₂-B1 <1, -1< B₂<1. Show that roots ₁ and 2 are complex if B1 + 4 B₂<0. Graph this regions implied by these inequalities.

An AR(2) time series, {x,: t€T}, if | 7₁ |>1 and | 7₂ |>1, where ₁ and 2 are the roots ofthe polynomial 1 - B₁ x - ₂x² = 0. Show that an AR(2) time series is stationary if the parameters, ß₁ and ß2, satisfy the following inequalities: B₂+ B1 <1, B₂-B1 <1, -1< B₂<1. Show that roots ₁ and 2 are complex if B1 + 4 B₂<0. Graph this regions implied by these inequalities.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Really want to understand the logic as well 

An AR(2) time series, {x¡ : t €T}, if|r₁ |>1 and | 1₂ |>1, where 7₁ and 72 are the roots ofthe polynomial 1 - B₁ x - B₂x² = 0. Show that an AR(2) time series is stationary if the parameters, ₁ and ß2, satisfy the following inequalities: B₂+ B1 <1, B₂-B1 <1, -1 < B₂ <1. Show that roots r₁ and 12 are complex if ß1 + 4 B₂ <0. Graph this regions implied by these inequalities.
Transcribed Image Text:An AR(2) time series, {x¡ : t €T}, if|r₁ |>1 and | 1₂ |>1, where 7₁ and 72 are the roots ofthe polynomial 1 - B₁ x - B₂x² = 0. Show that an AR(2) time series is stationary if the parameters, ₁ and ß2, satisfy the following inequalities: B₂+ B1 <1, B₂-B1 <1, -1 < B₂ <1. Show that roots r₁ and 12 are complex if ß1 + 4 B₂ <0. Graph this regions implied by these inequalities.
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